The formation of cracks in quasi-brittle materials such as concrete produces a degradation in mechanical performance in terms of both stiffness and strength. In addition to this, the presence of cracks leads to significant durability problems, such as reinforcement corrosion and calcium leaching [1]. Self-healing systems are designed to mitigate these issues by introducing crack 'healing' mechanisms into the material that result in a recovery of both mechanical performance and durability properties. There is now a significant body of work on the numerical simulation of self-healing systems [2-19], as highlighted in a recent review article [20]. The numerical treatment of damage-healing behaviour in mechanical self-healing models has varied, with many utilising a continuum damage-healing mechanics framework (e.g. [5, 7]). Alternative approaches have included a model based on micromechanical theories [11], the discrete element method (DEM) [13], the extended finite element method (XFEM) [12] and embedded discontinuity elements (EFEM) [17]. In addition to this, the treatment of the healing itself has varied, ranging from treating the healing as a thermodynamic

The presented adaptive modelling approach aims to jointly control the level of refinement for each of the building-blocks employed in a typical chain of finite element approximations for stochastically parametrized systems, namely: (i) finite error approximation of the spatial fields (ii) surrogate modelling to interpolate quantities of interest(s) in the parameter domain and (iii) Monte-Carlo sampling of associated probability distribution(s). The control strategy seeks accurate calculation of any statistical measure of the distributions at minimum cost, given an acceptable margin of error as only tunable parameter. At each stage of the greedy-based algorithm for spatial discretisation, the mesh is selectively refined in the subdomains with highest contribution to the error in the desired measure. The strictly incremental complexity of the surrogate model is controlled by enforcing preponderant discretisation error integrated across the parameter domain. Finally, the number of Monte-Carlo samples is chosen such that either (a) the overall precision of the chain of approximations can be ascertained with sufficient confidence, or (b) the fact that the computational model requires further mesh refinement is statistically established. The efficiency of the proposed approach is discussed for a frequency-domain vibration structural dynamics problem with forward uncertainty propagation. Results show that locally adapted finite element solutions converge faster than those obtained using uniformly refined grids.